Worked solution · Exam P
This Exam P sample reference tests Uniform Distribution. The no-deductible mean identifies the uniform support as [1,19]. A deductible of 4 leaves a positive excess over a 15-unit interval; integrating that excess against density 1/18 gives 225/36=6.25, so choice B is correct.
Independent solution
Setup
Use the no-deductible expected payment to recover the lower endpoint of the uniform loss distribution.
Model
The loss therefore has constant density 1/18 on [1,19], and the second policy pays only the positive excess above 4.
Compute
Integrate the payment over the part of the support above the deductible.
Answer
The expected payment under the deductible policy is 6.25.
Test the method on unseen problems
30 original univariate random variables problems with complete solutions and wrong-choice analysis. Written for Exam P, not copied from the SOA set. One-time $19 PDF.
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Original practice · fully worked
A research vessel's repair-cost index X is uniformly distributed from 0 to 24. A reserve pays the amount of X above an unknown activation threshold d and pays zero otherwise. The expected reserve payment is 3. Determine d.
For a uniform index on [0,24], the expected positive excess over d is (24-d)²⁄⁴⁸. Equating this to 3 gives 24-d=12 and hence d=12, so choice C is correct.
Setup
Represent the reserve payment as the positive part above the unknown threshold.
Model
Integrate the excess payment using the constant uniform density.
Compute
Set the expected payment equal to its specified value and retain the threshold within the support.
Answer
The reserve activates at a cost index of 12.
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These references share syllabus concepts or sit nearby in the official sequence. All 387 Exam P univariate random variables practice problems.
Drill the method: Exam P Uniform Distribution problems
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